相关论文: The mixmaster universe is chaotic

The Mixmaster or Bianchi IX cosmological model has become one of the archetypal settings for studying gravitational dynamics. The past decade has seen a vigourous debate about whether or not the Mixmaster's dynamics is chaotic. In this talk…

When gravitational fields are at their strongest, the evolution of spacetime is thought to be highly erratic. Over the past decade debate has raged over whether this evolution can be classified as chaotic. The debate has centered on the…

The significant discussion about the possible chaotic behavior of the mixmaster cosmological model due to Cornish and Levin [J.N. Cornish and J.J. Levin, Phys. Rev. Lett. 78 (1997) 998; Phys. Rev. D 55 (1997) 7489] is revisited. We improve…

The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here we present a variety of invariant measures for quantifying chaotic dynamics in relativity by exploiting the coordinate…

We show that the dynamics of a spatially closed Friedmann - Robertson - Walker Universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is…

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…

This paper provides a review of some recent issues on the Mixmaster dynamics concerning the features of its stochasticity. After a description of the geometrical structure characterizing the homogeneous cosmological models in the Bianchi…

All inhabitants of this universe, from galaxies to people, are finite. Yet the universe itself is often assumed to be infinite. If instead the universe is topologically finite, then light and matter can take chaotic paths around the compact…

In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…

Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner approach, showing how the chaotic behavior characterizing the evolution of the system near…

The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…

Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…

We provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner Hamiltonian approach, showing the covariant nature of its chaotic behaviour with respect to the choice of any time…

The chaoticity of the Mixmaster is discussed in the framework of Statistical Mechanics by using Misner--Chitre-like variables and an ADM reduction of its dynamics. We show that such a system is well described by a microcanonical ensemble…

We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial geometry and an extra non-compact coordinate. Finding a new class of solutions, we examine and rule out the possibility of deterministic chaos. We interpret this…

An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…

Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…

The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…

Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…

As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are…